mathlinks: grade 6 student packet 4 decimal ... grade/red...decimal concepts 4.2 decimal place value...

Name ___________________________ Period _________ Date ____________

MathLinks: Grade 6 (Student Packet 4)

4.1 Fractions and Decimals Use an area model to explore fraction and decimal concepts. Represent fractions and decimals using pictures, numbers, and

words. Link fraction notation to decimal notation. Write decimals in expanded forms.

1

4.2 Decimal Place Value and Number Lines Compare and order decimals. Locate decimals on a ruler and on a number line.

6

4.3 Fraction, Decimal, and Percent Gardens Rename fractions as decimals and percents. Know that percent means parts of a hundred.

13

4.4 Skill Builders, Vocabulary, and Review 19

6-4 STUDENT PACKET

MATHLINKS: GRADE 6 STUDENT PACKET 4 DECIMAL CONCEPTS

Decimal Concepts

MathLinks: Grade 6 (Student Packet 4) 0

WORD BANK

Word or Phrase Definition or Description Example or Picture

area model for fractions

decimal

denominator

equivalent fractions

fraction

linear model for fractions

numerator

percent

place value

Decimal Concepts 4.1 Fractions and Decimals


FRACTIONS AND DECIMALS

Summary We will represent fractions and decimals with pictures (area models), numbers, and words. We will write fractions whose denominators are powers of 10 in decimal form.

Goals

Use an area model to explore fraction and decimal concepts.

Represent fractions and decimals using picture, numbers, and words.

Link fraction notation to decimal notation.

Write decimals in expanded forms.

Warmup

1. Here are some pictorial representations of base-10 blocks.

If the small square has a value of 1 unit, then…

what is the value of the stick? _______

or

…and the value of the big square? ______ or

2. Shade the big square below to show that 40 = 4(10). Explain.

3. Shade the big square below to show that 82 = 8(10) + 2. Explain.



TENTHS AND HUNDREDTHS Here are some pictorial representations of “base-10 blocks.” If this big square has a value of 1 unit, then…

1. What is the value of this

shaded part?

2. What is the value of this

shaded part?

The big square has a value of 1. Use the base-10 values above to name these shaded parts using words and as fractions. 3.

4.

5.

6. 7. 8.

9. Which fractions from problems 3 – 8 represent the same value? How do you know?



THE BASE-10 PLACE VALUE SYSTEM Our place value number system is a positional number system in which the value of a digit in the number is determined by its location or place. In our “base-10” place value system, each place represents a power of 10.

Name of the place h

un

dre

ds

ten

s

on

es

ten

ths

hu

nd

red

ths

tho

usa

nd

ths

Value of the place (fraction form)

100 10 1

10

1

100

,

1

1 000

Value of place (decimal form)

100 10 1 0.1 0.01 0.001

1. Put a decimal point ( ) in its correct location above. The decimal point separates the whole

number part (to the left) from its fraction part (to the right). For the number, 7 2 3 . 0 4 5 : 2. Write the whole number part in words. 3. What is the value of the 2? _______________ __________ _______________ in words as a number in expanded form 4. Write the part after the decimal in words. 5. Write the part after the decimal as a fraction. 6. Write the entire number in words. 7. Write the entire number as a mixed number.

1



LINKING FRACTIONS AND DECIMALS

represents 1 represents 0.1 = 1

1 0 represents 0.01 = 1

100

Any fraction whose denominator is a power of 10 can be written as a decimal. Write each pictorial representation using words, in fraction form, and in decimal form. Diagram Words Fraction Decimal 1.

Twenty-three hundredths 23

100 0.23

2.

3.

4.

5.

6. Problem # _____ and problem # _____ represent equivalent fractions. Write these

equivalents as fractions and decimals.

______ = ______ = ______ = ______ fraction fraction decimal decimal

Use the pictorial representations above to support your answers. 7. Explain why the following statement is incorrect: 0.23 > 0.3. 8. Why is 0.03 smaller than 0.3?



EXPANDED FORMS OF DECIMALS The standard form for a decimal is given. Write each number in three different expanded forms. Expanded Form #1 Expanded Form #2 Expanded Form #3

1.

20.65

20 + 0.6 + 0.05

20.65

2(10) + 6

1

10 + 5

1

100

20.65

2(10) + 6(0.1) + 5(0.01)

2.

0.849 0.849 0.849

3.

53.07 53.07 53.07

4.

106.004 106.004 106.004

Each number below is written in an expanded form. Write the number in standard form. 5. 8 + 0.06 + 0.005 6. 2(100) + 3(1) + 9(0.01)

7. 71

1,000

+ 4

1

10 + 2(1)

8. Eduardo says that 48.76 = 48 + 0.7 + 0.06 is in “Expanded Form #1.” Explain why he is

not correct and write the statement correctly in “Expanded Form #1.”

Decimal Concepts 4.2 Decimal Place Value and Number Lines


DECIMAL PLACE VALUE AND NUMBER LINES

Summary

We will compare and order decimals on a number line and on a ruler.

Goals Compare and order decimals. Locate decimals on a ruler and on a

number line.

Warmup

1. Place the decimal point in its proper location on the place value chart.

Name of the place

hu

nd

red

s

ten

s

on

es

ten

ths

hu

nd

red

ths

tho

usa

nd

ths

Value of the place (fraction form)

100 10 1

10

1

100

,

1

1 000

Value of the place (decimal form)

100 10 1 0.1 0.01 0.001

2. Write the number 4 3 6 . 9 1 7 in words.

3. Circle the digit in the tens place. 4 3 6 . 9 1 7

4. Circle the digit in the tenths place. 4 3 6 . 9 1 7

5. Circle the digit in the hundreds place. 4 3 6 . 9 1 7

6. Circle the digit in the hundredths place. 4 3 6 . 9 1 7 7. Circle the digit in the ones place. 4 3 6 . 9 1 7 8. Circle the digit in the thousandths place. 4 3 6 . 9 1 7

1



READING A METERSTICK A meterstick (about the length of a baseball bat) can be thought of as a number line representation for decimals between zero and one.

1. A decimeter (about the length of a cell phone) is one-tenth (0.1 = 1

10 ) of a meter. Use

decimal notation to label this reduced meterstick in tenths of a meter.

2. Graph and label the following points above.

Point A: 0.1 meters Point B: 0.9 meters Point C: 0.55 meters

3. A centimeter (about the diameter of a pencil) is one hundredth (0.01 = 1

100 ) of a meter.

Use decimal notation to label this enlarged decimeter stick in hundredths of a meter.


Point D: 0.01 meters Point E: 0.07 meters Point F: 0.025 meters

5. A millimeter (about the thickness of a dime) is one thousandth (0.001 = 1

1,000) of a meter.

Use decimal notation to label this enlarged centimeter stick in thousandths of a meter.


Point G: 0.001 meters Point H: 0.006 meters Point J: 0.0075 meters

0 meters 1 meter

0 meters 0.1 meter or 1 decimeter

0 meters 0.01 meter or 1 centimeter



READING A METERSTICK (Continued) Use decimal notation to mark all tick marks and end points on each measurement stick. 7. 8. 9. 10. Use the measurement sticks above to help you answer these questions. 11. What length is half way between 0.3 meters and 0.4 meters? _____________________

Write this length in words. 12. Randall says that 0.17 > 0.2 because 17 > 2. Is he correct? ______ Explain. 13. Candy says that 0.93 meters = 0.930 meters. Is she correct? ______ Explain.

0.4 meters 0.3 meters

0.1 meters 0.2 meter





ORDERING NUMBERS BETWEEN 0 AND 1

1. Circle all of the numbers that have the same value as 0.3.

3

10 3 tens

30

100 0.03 30 hundredths 0.3003 tenths 0.30

Order these numbers from least to greatest.

2. 0.240 0.56 0.8 0.111 0.099

________ < ________ < ________ < ________ < ________

3. 0.7 0.32 0.07 0.032 0.145

________ < ________ < ________ < ________ < ________

Label the number lines below using the scales provided. Then write letters above the number lines to estimate the placement of the given numbers. 4. (A) 0.51 (B) 0.25 (C) 0.32 (D) 0.99 (E) 0.01 0 1 5. (F) 0.011 (G) 0.025 (H) 0.029 (J) 0.049 (K) 0.099 0 0.1 Label the number lines below using the scales provided. Then write letters above the number lines to estimate the placement of the given numbers.

6. (L) 0.081 (M) 0.75 (N) 0.38 (P) 0.5 (R) 0.05

7. (T) 0.111 (U) 0.125 (V) 0.159 (W) 0.10 (Y) 0.2



PRACTICE ORDERING NUMBERS BETWEEN 0 AND 1

1. Circle all of the numbers that have the same value as 0.70.

70 tenths 0.7 7

10 7 tens

7

100 0.07 70 hundredths 0.700

Order these numbers from least to greatest. 2. 0.8 0.214 0.08 0.021 0.42

________ < ________ < ________ < ________ < ________

3. 0.19 0.019 0.91 0.901 0.109

________ < ________ < ________ < ________ < ________

Label the number lines below using the scales provided. Then write letters above the number lines to estimate the placement of the given numbers.

4. (A) 0.11 (B) 0.89 (C) 0.40 (D) 0.65 (E) 0.56

0 1 5. (F) 0.015 (G) 0.021 (H) 0.079 (J) 0.044 (K) 0.089 0 0.1 Label the number lines below using the scales provided. Then write letters above the number lines to estimate the placement of the given numbers. 6. (L) 0.21 (M) 0.45 (N) 0.78 (P) 0.80 (Q) 0.08

7. (R) 0.115 (T) 0.129 (U) 0.160 (V) 0.100 (W) 0.200



ORDERING NUMBERS ON A NUMBER LINE Label the number lines below using the scales provided. Then write letters above the number lines to estimate the placement of the given numbers. 1. (A) 1.05 (B) 1.50 (C) 3.9 (D) 9.3 (E) 0.56

0 10

2. (F) 10.015 (G) 3.4 (H) 12.75 (J) 1.1 (K) 15.9 0 10 3. (L) 2.25 (M) 4.025 (N) 3.5 (O) 0.05 (P) 0.9 0 3 Label the number lines below using the scales provided. Then write letters above the number lines to estimate the placement of the given numbers. 4. (Q) 0.09 (R) 0.9 (S) 0.99 (T) 0.05 (U) 0.50

5. (V) 0.105 (W) 0.150 (X) 0.100 (Y) 0.199 (Z) 0.19

6. (F) 0.5 (G) 0.05 (H) 5.55 (J) 15.75 (K) 17.95



ORDER IT! AGAIN

Play this game with a partner.

You Will Need: 2 or more players 32 or more Fraction Cards and Decimal Cards The object of this game is to get five numbers in a row, in order, from least value to greatest value. Once a card is placed on the table face up, it may not be moved to another location. However, a new card may be placed on top of it. Shuffle all the cards and place the cards face-down in a pile. To begin, put 5 cards face-up, in the order they are drawn. The first player draws a card from the pile and places it on top of one of the existing face

up cards. If all of the cards are now in order from least to greatest, then the player wins. If not, then play continues until all five cards are in order from least to greatest.

The next player draws a card from the pile and places it on top of one of the existing face-up cards. If all the cards are now in order from least to greatest, then the player wins. If not, then play continues until all five cards are in order from least to greatest.

In order to win, a player must convince his or her opponent with a reasonable argument that the cards are in order.

1. Play two rounds of the Order It! Record one of the ordered card sequences here.

__________ __________ __________ __________ __________ 2. Explain why the numbers are in order.

Decimal Concepts 4.3 Fractions, Decimal, and Percent Gardens


FRACTION, DECIMAL, AND PERCENT GARDENS

Summary We will use an area model to explore fraction, decimal, and percent concepts.

Goals Rename fractions as decimals and

percents. Know that percent means parts of a

hundred.

Go

Zachary, Alexandra, and Lily have the same size gardens. Zachary’s Garden Alexandra’s Garden Lily’s Garden 1. Whose garden has the greatest area? Zachary planted one-half of his garden. Alexandra planted three-fourths of her garden. Lily planted three-eighths of her garden. 2. Shade in the planted areas of their gardens. 3. Use numbers to write the planted areas of each garden as a fraction. 4. Whose garden has the greatest planted area? 5. Whose garden has the least planted area? 6. Estimate the correct location of the fractions on the number line below. Explain how you

know the correct order.

0 1



GARDENS 1 For each problem, the shaded part in figure A is given as a fraction. Shade figure B so that the same fractional part is shaded. 1. 2.

A

A

B B

17 =

50 100= _____% = _____ 17

= 25 100

= _____% = _____

fraction percent decimal fraction percent decimal 3. 4.

A A

B B

3 =

5 100= _____% = _____ 3

= 10 100

= _____% = _____

fraction percent decimal fraction percent decimal

5. Which of the fractions above are greater than 1

2? Explain.




A A

B B

7 =

20 100= _____% = _____ 17

= 20 100

= _____% = _____


3. Which fraction is greater: 720

or 1720

? Explain.

4. 5. A A

B B

3 =

4 100= _____% = _____ 4

= 5 100

= _____% = _____


6. Which fraction is greater: 3

4 or 4

5? Explain.




A A

B B

1 =

2 100= _____% = _____ 1

= 4 100

= _____% = _____

fraction percent decimal fraction percent decimal 3. 4.

A A

B B

1

8 is about = _____% = _____ 1

16 is about = _____% = _____

fraction percent decimal fraction percent decimal 5. Order the fractions above from least to greatest. Explain.

100 100



STRAWBERRY GARDENS

Judy and Jane planted strawberries in their gardens. Judy planted 115

of her garden. Jane

planted 710

of her garden. Shade the planted part of each garden on the hundred-square grid.

1. Judy’s Garden 2. Jane’s Garden

a. How many squares did you shade?

b. The shaded part is what fraction of the whole square?

c. Write the fraction as a decimal and as a percent.






PUMPKIN PATCHES

Eden and Alan planted pumpkin patches. Eden planted 22

of her patch. Alan planted 38

of his

patch. Shade the planted part of each pumpkin patch on the hundred-square grids.

1. Eden’s Pumpkin Patch 2. Alan’s Pumpkin Patch



c. Write the fraction as a decimal and

as a percent.




Decimal Concepts 4.4 Skill Builders, Vocabulary, and Review


SKILL BUILDERS, VOCABULARY, AND REVIEW

SKILL BUILDER 1

1. Write inequalities using the < symbol to compare the unit fractions below. 1 1 1 1

, , , , 2 3 4 6

and 1

8

_______ < _______ < _______ < _______ < _______

2. Write inequalities using the < symbol to compare the fractions below.

2 2 2, , ,

8 4 6 and 2

2 _______ < _______ < _______ < _______

3. Estimate the location of each number on the number line.

3 3 3 1 15 180 1

5 7 9 6 20 19

4. Explain how you located the fractions 1520

and 1819

on your number line.

Rewrite each measurement as an improper fraction.

5. 1 1

4 in. 6. 1 3

8 in. 7. 4 3

8 in.

Rewrite each measurement as a mixed number.

8. 7

2 in. 9.

19

2 in. 10.

46

5 in.



7 4 2 3

SKILL BUILDER 2 Begin with any small whole number. Multiply your number by 10. Multiply the result by 12. Multiply that result by 54. Multiply that result by 56. (You should have a big number now!) 1. I began with the number ______. After multiplying, my big number is ___________.

2. Start with your big number. Divide it by 12. Divide that result by 21. Divide that result by

32. Divide that result by 45. After dividing I got _____.

3. Start with your same big number from problem 1. Divide it by 6. Divide that result by 20. Divide that result by 42. Divide that result by 72. After dividing I got _____.

4. Did you get the same results for problems 2 and 3? Explain why you think this happened.

5. Find the perimeter of the figure to the right. 6. What is the perimeter of a rectangle with a width of 5 cm and a length of 9 cm?



SKILL BUILDER 3

1. List all the factors of 42. ___________________________________________________ 2. List all the factors of 28. ___________________________________________________ 3. In problems 1 and 2, circle all the factors that 42 and 28 have in common.

The greatest factor that 42 and 28 have in common is _____. 4. Describe in your own words why the number you wrote for problem 3 is the greatest

common factor (GCF) of 42 and 28. 5. Use the process described above to find the GCF of 66 and 110. 6. List the first ten multiples of 8. ______________________________________________ 7. List the first ten multiples of 6. ______________________________________________ 8. In problems 6, and 7, circle all the multiples that 8 and 6 have in common.

The least multiple that 8 and 6 have in common is _____. 9. Describe in your own words why the number you wrote for problem 8 is the least common

multiple (LCM) of 8 and 6. 10. Use the process described above to find the LCM of 8 and 12. 11. Use ANY process to find the GCF and the LCM of 18 and 24.



SKILL BUILDER 4

Evaluate each expression.

List the operations in order from first to last.

1. 12 6

4 + 2

2. 4 – 12 ÷ 3 + 1 • 3

Any fraction whose denominator is a power of 10 can be written as a decimal. Write each pictorial representation using words, in fraction form, and in decimal form. Assume the area of the big square is equal to 1. Diagrams Words Fraction Decimal 3.

4.

5.

6.

7.

8. Problem # _____ and problem #_____ represent equivalent fractions. Write these

equivalents as fractions and decimals.

______ = ______ = ______ = ______ fraction fraction decimal decimal



SKILL BUILDER 5 1. Write 310.567 using words. The standard form for a decimal is given. Write each number in three different expanded forms. Expanded Form #1 Expanded Form #2 Expanded Form #3

2. 24.65

24.65

24.65

3. 154.06 154.06 154.06

4. 0.904 0.904 0.904

For problems 5-7, write each expanded form number in its standard form. 5. 80 + 0.07 + 0.005 6. 100 + 7 + 0.08 7. 0.006 + 20 + 0.5

8. Shantrelle incorrectly thinks that 0.32 < 0.164 because 32 < 164. Write an explanation that could help Shantrelle understand her mistake.



SKILL BUILDER 6 1. Circle all of the numbers that have the same value as 0.7.

7

10 7 tens 70 hundredths

70

100 0.07

Order these numbers from least to greatest. 2. 0.360 0.56 0.9 0.222 0.09999

________ < ________ < ________ < ________ < ________

3. 0.7 0.007 0.07 0.77 0.7077

________ < ________ < ________ < ________ < ________

Label the number lines below using the scales provided. Then write letters above the number lines to estimate the placement of the given numbers. 4. (A) 0.41 (B) 0.75 (C) 0.33 (D) 0.799 (E) 0.11 5. (F) 0.015 (G) 0.021 (H) 0.049 (J) 0.0909 (K) 0.0999 6. Label the number line below using the scales provided. Then write letters above the

number line to estimate the placement of the given numbers.

(L) 1.5 (M) 1.1 (N) 1.9 (P) 1.05 (Q) 1.75 (R) 1.32

0 1

0 0.1



SKILL BUILDER 7 Jamal and David planted flowers in their gardens. Jamal planted 3

5 of his garden. David

planted 34

of his garden.

Shade the planted part of each garden on the hundred-square grid. 1. Jamal’s Garden 2. David’s Garden

90090*/f

a. How many squares did you shade? b. The shaded part is what fraction of the

whole square? c. Write the fraction as a decimal and as a

percent.

a. How many squares did you shade? b. The shaded part is what fraction of the

whole square? c. Write the fraction as a decimal and as a

percent.

3. Chris has planted 710

of his garden. Who has planted the greatest part of their gardens,

Jamal, David, or Chris? Explain your reasoning.



FOCUS ON VOCABULARY

Across Down

4 Positional number system where the value of a digit is determined by its location

1 Measurement for division of whole numbers

7 Model that uses a number line 2 6.5, for example

8 Two fractions that represent the same point on the number line

3 8 in the number 6

8

9 Place to right of decimal 5 Model based on the size of the partitions of a figure

10 6 in the number 6

8 6 Per hundred



SELECTED RESPONSE Show your work on a separate sheet of paper.

1. Choose all statements that are true for the number 302.14.

A. The 3 is in the hundreds place. C. The 4 is in the tenths place.

B. It is equivalent to 300 + 2 + 0.1 + 0.04. D. It is larger than 302.7.

2. Choose all of the statements that are true.

A. 0.77 < 0.077 < 0.0777 < 7.0 C. 0.077 < 0.0777 < 0.77 < 7.0

B. 0.077 < 0.77 < 0.0777 < 7.0 D. 7.0 < 0.77 < 0.077 < 0.0777

3. Choose all of the answers that illustrate the portion of the figure that is shaded to the right.

A. 75% B. 75

100

C. 0.75 D. 3

4

4. Choose all of the following expressions that are equivalent to 203.14.

A. 203 + 0.14 C. 2(100) + 3(1) + 10(.1) + 4(0.01)

B. 2 + 0 + 3 +0 .1 +0 .4 D. 200 + 3 + 0.1 + 0.04

5. Choose all of the following that are between 50.60 and 50.63

A. 51.63 B. 50.6 C. 50.9 D. 50.66 E. 50.608



KNOWLEDGE CHECK Show your work on a separate sheet of paper and write your answers on this page. 4.1 Fractions and Decimals 1. Write the number 0.789 as a fraction. 2. Write the number 900 + 7 + 0.1 + 0.009 in standard form. 3. Write the number 9(10) + 6(0.01) + 4(0.1) + 5(100) in standard form. 4.2 Decimal Place Value and Number Lines Label the number lines below using the scales provided. Then write letters above the number lines to estimate the placement of the given numbers. 4. (A) 2.05 (B) 2.50 (C) 5.05 (D) 9.99 (E) 9.09

5. (F) 10.91 (G) 10.091 (H) 1.9 (J) 11.9 (K) 19.1 4.3 Fraction, Decimal, and Percent Gardens 6. Write a fraction to represent the portion of figure A that is

shaded. 7. Shade figure B so that the same fractional part

is shaded as in figure A. 8. Write a fraction, a decimal, and a percent

representing the portion of figure B that is shaded.

A

B

0 10

0 10



HOME SCHOOL CONNECTION Here are some questions to review with your young mathematician. 1. Fill in the decimal value for each rectangle in the table below. Then explain if any have the

same value, and why.

Picture Decimal Value

A 1

B

C

D

2. Label the number line below using the scales provided. Then write letters above the

number line to estimate the placement of the given numbers. A. 0.5 B. 1.3 C. 1.9 D. 0.05 E. 1.45

3. Write a fraction to represent the portion of figure A

that is shaded. Shade figure B so that the same fractional part is shaded. Write a fraction, a decimal, and a percent representing the portion of figure B that is shaded.

A

B

A B

C

D

0 2

Parent (or Guardian) Signature _____________________________

Decimal Concepts


COMMON CORE STATE STANDARDS – MATHEMATICS

STANDARDS FOR MATHEMATICAL CONTENT

3.NF.3d* Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size: Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

4.NF.6* Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

5.NBT.1* Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

5.NBT.3a* Read, write, and compare decimals to thousandths: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).

5.NBT.3b* Read, write, and compare decimals to thousandths: Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

*Review of content essential for success in 6th grade.

STANDARDS FOR MATHEMATICAL PRACTICE

MP5 Use appropriate tools strategically.

MP7 Look for and make use of structure.

MP8 Look for and express regularity in repeated reasoning.

© 2015 Center for Math and Teaching

mathlinks: grade 6 student packet 4 decimal ... grade/red...decimal concepts 4.2 decimal place value...

Documents